Training automatic modulation classification (AMC) models on centrally aggregated data raises privacy concerns, incurs communication overhead, and often fails to confer robustness to channel shifts. Federated learning (FL) avoids central aggregation by training on distributed clients but remains sensitive to class imbalance, non-IID client distributions, and limited labeled samples. We propose FedSSL-AMC, which trains a causal, time-dilated CNN with triplet-loss self-supervision on unlabeled I/Q sequences across clients, followed by per-client SVMs on small labeled sets. We establish convergence of the federated representation learning procedure and a separability guarantee for the downstream classifier under feature noise. Experiments on synthetic and over-the-air datasets show consistent gains over supervised FL baselines under heterogeneous SNR, carrier-frequency offsets, and non-IID label partitions.